Baryonic symmetries and M5 branes in the AdS_4/CFT_3 correspondence

TL;DR

This paper explores U(1) symmetries in the AdS_4/CFT_3 correspondence for M2 branes, analyzing boundary conditions, baryonic operators, and M5 brane states, with detailed examples and implications for non-perturbative effects.

Contribution

It provides a detailed analysis of baryonic symmetries, boundary conditions, and wrapped M5 branes in the AdS_4/CFT_3 context, including explicit computations for specific singularities.

Findings

Agreement between gauge-invariant operators and wrapped M5 branes

Matching of condensates, Goldstone bosons, and strings in symmetry-breaking vacua

Explicit formula for M5 instanton actions related to harmonic two-forms

Abstract

We study U(1) symmetries dual to Betti multiplets in the AdS_4/CFT_3 correspondence for M2 branes at Calabi-Yau four-fold singularities. Analysis of the boundary conditions for vector fields in AdS_4 allows for a choice where wrapped M5 brane states carrying non-zero charge under such symmetries can be considered. We begin by focusing on isolated toric singularities without vanishing six-cycles, and study in detail the cone over Q^{111}. The boundary conditions considered are dual to a CFT where the gauge group is U(1)^2 x SU(N)^4. We find agreement between the spectrum of gauge-invariant baryonic-type operators in this theory and wrapped M5 brane states. Moreover, the physics of vacua in which these symmetries are spontaneously broken precisely matches a dual gravity analysis involving resolutions of the singularity, where we are able to match condensates of the baryonic operators, Goldstone bosons and global strings. We also argue more generally that theories where the resolutions have six-cycles are expected to receive non-perturbative corrections from M5 brane instantons. We give a general formula relating the instanton action to normalizable harmonic two-forms, and compute it explicitly for the Q^{222} example. The holographic interpretation of such instantons is currently unclear.